This paper shows that quantifier scope phenomena can be precisely charac- terized by a semantic representation cons- trained by surhce constituency, if the di- stinction between referent
Trang 1Quantifier Scope and Constituency
J o n g C P a r k
C o m p u t e r a n d I n f o r m a t i o n S c i e n c e
U n i v e r s i t y of P e n n s y l v a n i a
200 S o u t h 3 3 r d S t r e e t , P h i l a d e l p h i a , P A 19104-6389, U S A
park@line, cis upenn, edu
A b s t r a c t Traditional approaches to quantifier scope
typically need stipulation to exclude rea-
dings that are unavailable to human under-
standers This paper shows that quantifier
scope phenomena can be precisely charac-
terized by a semantic representation cons-
trained by surhce constituency, if the di-
stinction between referential and quantifi-
cational NPs is properly observed A CCG
implementation is described and compared
to other approaches
1 I n t r o d u c t i o n
It is generally assumed that sentences with multi-
ple quantified NPs are to be interpreted by one or
more unambiguous logical forms in which the scope
of traditional logical quantifiers determines the rea-
ding or readings There are two problems with this
assumption: (a) without further stipulation there is
a tendency to allow too many readings and (b) there
is considerable confusion as to how many readings
should be allowed arising from contamination of the
semantics of many NL quantifiers by referentiality
There are two well-known techniques for redis-
tributing quantifiers in quantification structures:
quantifying-in (Montague, 1974; Cooper, 1983; Kel-
ler, 1988; Carpenter, 1994) and quantifier raising
(May, 1985) The former provides a compositio-
nal way of putting possibly embedded quantifiers
to the scope-taking positions, and the latter utili-
zes a syntactic movement operation at the level of
semantics for quantifier placement There are also
approaches that put more emphasis on utilizing con-
textual information in restricting the generation of
semantic forms by choosing a scope-neutral repre-
sentation augmented with ordering constraints to
capture linguistic judgments (Webber, 1979; Kamp,
1981; Helm, 1983; Poesio, 1991; Reyle, 1993) And
there are computational approaches that screen una-
vailable and/or redundant semantic forms (Hobbs
Shieber, 1987; Moran, 1988; Vestre, 1991) This pa-
per will show that these approaches allow unavaila-
ble readings, and thereby miss an important gene- ralization concerning the readings that actually are available
This paper examines English constructions that allow multiple occurrences of quantified NPs: NP modifications, transitive or ditransitive verbs, that
complements, and coordinate structures Based on
a critical analysis of readings that are available from these data, the claim is that scope phenomena can
be characterized by a combination of syntactic sur- face adjacency and semantic function-argument re- lationship This characterization will draw upon the old distinction between referential and quantificatio- nal NP-semantics (Fodor & Sag, 1982) We choose
to use Combinatory Categorial Grammar to show how surface adjacency affects semantic function- argument relationship, since CCG has the flexibility
of composing almost any pair of adjacent constitu- ents with a precise notion of syntactic grammatica- lity (Steedman, 1990; 1993) z
The rest of the paper is organized as follows First,
we discuss in §2 how traditional techniques address availability of readings and note some residual pro- blems Then we give a brief analysis of available readings (§3), a generalization of the analysis (§4), and finally describe a computational implementation
in Prolog (~5)
2 T r a d i t i o n a l A p p r o a c h e s All three paradigms of grammar formalisms intro- duced earlier share similar linguistic judgments for their grammaticality analyses This section exami- nes quantifying-in to show (a) that quantifying-
in is a powerful device that allows referential NP- interpretations and (b) that quantifying-in is not suf- ficiently restricted to account for the available rea- dings for quantificational NP-interpretations Quantifying-in is a technique originally introdu- ced to produce appropriate semantic forms for de
re interpretations of NPs inside opaque operators
1 For instance, the result would transfer to Synchro- nous "I~ee Adjoining Grammar (Shieber & Schabes, 1990) without much change
Trang 2(Montague, 1974) For example, (a) below has two
readings, de re and de dicto, depending on the rela-
tivity of the existence of such an individual They
are roughly interpretable as (b) and (@2
(1) (a) John believes that a Republican will win
(b) 3r.repub(r) A bel(john, u i l l ( u i n ( r ) ) )
(C) bel(john, 3r.repub(r) A uill(uin(r)))
(b) has a binder 3 that is quaati.fving a variable r
inside an opaque operator b e l , hence the name for
the technique (c) does not have such an interven-
ing operator Although it is beyond the scope of the
present paper to discuss further details of intensio-
nality, it is clear that de re interpretations of NPs
are strongly related to referential NP-semantics, in
the sense that the de re reading of (a) is about a
referred individual and not about an arbitrary such
individual Quantifying-in is designed to make any
(possibly embedded) NP take the matrix scope, by
leaving a scoped variable in the argument position
of the original NP This would be acceptable for re-
ferential NP-semantics
Montague also proposed to capture purely exten-
sional scope ambiguities using quantifying-in For
example, wide scope reading of a w o m a n in (a) below
is accounted for by quantifying-in (with a meaning
postulate), patterned after one for (b)
(2) (a) Every man loves a woman
(b) Every man seeks a white unicorn
His suggestion is adopted with various subsequent
revisions cited earlier Since any NP, referential or
quantificational, requires quantifying-in to outscope
another, quantifying-in consequently confounds re-
ferential and quantificational NP-semantics This
causes a problem when there is a distributional dif-
ference between referential NPs and non-referential
NPs, as Fodor & Sag (1982) have argued, a view
which has been followed by the approaches to dy-
namic interpretation of indefinite NPs cited earlier
It seems hard to reconcile quantifying-in with these
observations
3 A v a i l a b i l i t y o f R e a d i n g s
This section proposes a way of sharpening our intui-
tion on available readings and re-examines traditio-
nal linguistic judgments on grammatical readings
While there are undoubted differences in degree
of availability among readings dependent upon se-
mantics or discourse preference (Bunt, 1985; Moran,
1988), we will focus on all-or-none structural possi-
bilities afforded by competence grammar 3
2In this simplistic notation, we gloss over tense ana-
lysis, among others
3Moran's preference-based algorithm treats certain
readings as "highly unpreferred," effectively making
them structurally unavailable, from those possible sco-
Consider the following unambiguous quantifica- tion structure in a generalized quantifier format (hereafter oq, Barwise & Cooper, 1981), where
q u a n t i f i e r outscopes any quantifiers that may oc-
cur in either r e s t r i c t i o n or body
(3) q u a n t i f i e r ( v a r i a b l e , r e s t r i c t i o n , body) Logical forms as notated this way make explicit the functional dependency between the denotations of two ordered quantificational NPs For example~ con- sider (4) (a) (Partee, 1975) (b) shows one way of representing it in a GQ format
(4) (a) Three Frenchmen visited five Russians (b) t h r e e ( f , frenchmen(f), f i v e ( r ,
russians (r), v i s i t e d ( f , r) ) )
We can always argue, by enriching the notation, that (4) (b) represents at least four different readings, de- pending on the particular sense of each involved NP, i.e., group- vs individual-denoting In every such reading, however, the truth of (4) (b) depends upon finding appropriate individuals (or the group) for f such that each of those individuals (or the group itself) gets associated with appropriate individuals (or a group of individuals) for r via the relation
v i s i l ; e d 4 Notice that there is always a f u n c t i o n a l
d e p e n d e n c y of individuals denoted by r upon indi- viduals denoted by f We claim that this explicit functional dependency can be utilized to test availa- bility of readings 5
First, consider the following sentences without coordination
(5) (a) Two representatives of three companies
saw most samples
(b) Every dealer shows most customers at most three cars
(c) Most boys think that every man d a n c e d with two women
(a) has three quantifiers, and there are 6 different ways of ordering them Hobbs & Shieber (1987) show that among these, the reading in which two re-
p r e s e n t a t i v e s outscopes m o s t s a m p l e s which in turn outscopes three c o m p a n i e s is not available from the sentence They attribute the reason to the logical structure of English as in (3), as it is considered unable to afford an unbound variable, a constraint known as the unbound variable constraint (uvc) 6
We should note, however, that there is one reading pings generated by a scheme similar to Hobbs & Shieber (1887) We clash that competence grammax makes even fewer readings available in the first place
4Without losing generality, therefore, we will consider only individual-denoting NPs in this paper
SSingular NPs such as a company are not helpful to this task since their denotations do not involve multi- ple individuals which explicitly induce this functional dependency
eThe reading would be represented as follows, which has the first occurrence of the variable c left unbound
2 0 6
Trang 3among the remaining five t h a t the u v c allows which
in fact does not appear to be available This is the
one in which three companies outscopes m o s t samp-
les which in turn outscopes two representatives (cf
Horn (1972), Fodor (1982)) 7 This suggests t h a t
the u v c m a y not be the only principle under which
Hobbs & Shieber's reading is excluded, s T h e other
four readings of (a) are self-evidently available If
we generalize over available readings, they are only
those t h a t have no quantifiers which intercalate over
NP boundaries 9
(5) (b) has three quantifiers too, b u t unlike (5)
(a), all the six ways of ordering the quantifiers are
available (5) (c) has only four available readings,
where m o s t boys does not intercalate every m a n and
t w o w o m e n 1°
Consider now sentences including coordination
(6) (a) Every girl admired, but most boys dete-
sted, one of the saxophonists
(b) Most boys think t h a t every m a n danced
with, b u t doubt t h a t a few boys talked to,
more t h a n two women
As Geach (1970) pointed out, (a) has only two gram-
matical readings, though it has three quantifiers In
reading 1, the same saxophonist was admired and
detested at the same time In reading 2, every girl
admired an arbitrary saxophonist and most boys
also detested an arbitrary saxophonist In particu-
lar, missing readings include the one in which every
girl admired the same saxophonist and most boys
detested the same but another saxophonist (6) (b)
t h r e e ( c , comp(c), s a g ( r , s ) ) ) )
7To paraphrase this impossible reading, it is true of a
situation under which there were three companies such
that there were four samples for each such company such
that each such sample was seen by two representatives of
that company Crucially, samples seen by representatives
of different companies were not necessarily the same
SThis should not be taken as denying the reality of the
uvc itself For example, as one of the referees pointed
out, the uvc is required to explain why, in (a) below,
every professor must outscope a friend so as to bind the
pronoun his
(a) Most students talked to a friend of every pro-
fessor about his work
9One can replace most samples with other complex
NP such as most samples of at least five products to see
this Certain sentences that apparently escape this ge-
nerafization will be discussed in the next section
1°To see why they are available, it is enough to see
that (a) and (b) below have two readings each
(a) 3ohn thinks that every man danced with two
women
(b) Most boys think that Bill danced with two
women
also has only two g r a m m a t i c a l readings In one,
m o s t boys outscopes every m a n and a f e w boys which together outscope more than two w o m e n In the other, more than two w o m e n outscopes every m a n
and a f e w boys, which together outscope m o s t boys
4 A n A c c o u n t o f A v a i l a b i l i t y This section proposes a generalization at the level of semantics for the p h e n o m e n a described earlier and considers its apparent counterexamples
Consider a language £ for natural language se- mantics t h a t explicitly represents function-argument relationships (Jackendoff, 1972) Suppose t h a t in £: the semantic form of a quantified N P is a syntactic argument of the semantic form of a verb or a pre- position (7) through (10) below show well-formed expressions in £.11
(7) v i s i t l d ( f i v e ( r u l s i i m ) , t h r s e ( f r e n c l u i i n ) )
(8) saw(most (sanp) ,of (thres(cmap) ,two(rap))) (9) show (three(car) ,most (cstmr), every(dlr)) (10) think(Adlmced(two(woman) , e v e r y ( n a n ) ) , most (boy))
For instance, o f has two arguments three(comp)
and t w o ( r e p ) , and show has three arguments /: gives rise to a natural generalization of available readings as summarized below 12
(11) For a function with n arguments, there are n! ways of successively providing all the ar- guments to the function
This generalization captures the earlier observations about availability of readings (7), for (4) (a), has two (2!) readings, as v i a i t e d has two arguments (8) is an abstraction for four (2!x2!) readings, as
b o t h o f and maw have two arguments each (9) is an abstraction for six (3!) readings, as show has three arguments Likewise, (10) is an abstraction for four readings
Coordination gives an interesting constraint on availability of readings Geach's observation that (6) (a) has two readings suggests t h a t the scope of the object must be determined before it reduces with the coordinate fragment Suppose t h a t the non- standard constituent for one of the conjuncts in (6) (a) has a semantic representation shown below (12) ~z a d n i r e d ( z , s v e r y ( g i r l ) )
Geach's observation implies that (12) is ambiguous,
so that every(girl) can still take wide (or narrow) scope with respect to the u n k n o w n argument A 11The up-operator ^ in (10) takes a term of type t to
a term of type e, but a further description of £ is not relevant to the present discussion
1 2 N a n (1991)'s work is based on a related observation, though he does not make use of the distinction between referential and quantificational NP-semantics
Trang 4theory of C C G will be described in the next sec-
tion to show h o w to derive scoped logical forms for
available readings only
But first we must consider some apparent coun-
terexamples to the generalization,
(13) (a) Three hunters shot at five tigers
(b) Every representative of a company saw
most samples
The obvious reading for (a) is called conjunctive or
cumulative (Partee, 1975; Webber 1979) In this
reading, there are three hunters and five tigers such
that shooting events happened between the two par-
ties Here, arguments are not presented in succes-
sion to their function, contrary to the present gene-
ralization Notice, however, that the reading must
have two (or more) referential NPs (Higginbotham,
1987) 13 The question is whether our theory should
predict this possibility as well For a precise notion
of availability, we claim that we must appeal to the
distinction between referential and quantificational
NP-semantics, since almost any referential NP can
have the appearance of taking the matrix scope, wi-
thout affecting the rest of scope phenomena A re-
lated example is (b), where in one reading a referen-
tial NP a company arguably outscopes most samples
which in turn outscopes every representative (Hobbs
& Shieber, 1987) As we have pointed out earlier,
the reading does not generalize to quantified NPs in
general
(14) (a) Some student will investigate two dia-
lects of every language
(b) Some student will investigate two dia-
lects of, and collect all interesting examp-
les of coordination in, every language
(c) * Two representative of at least three
companies touched, but of few universi-
ties saw, most samples
(a) has a reading in which every language outscopes
some student which in turn outscopes two dialects
(May, 1985) In a sense, this has intercalating NP
quantifiers, an apparent problem to our generaliza-
tion However, the grammaticality of (b) opens up
the possibility that the two conjuncts can be repre-
sented grammatically as functions of arity two, si-
milar to normal transitive verbs Notice that the
generalization is not at work for the fragment of at
least three companies touched in (c), since the con-
junct is syntactically ungrammatical At the end of
next section, we show how these finer distinctions
are made under the CCG framework (See discussion
of Figure 5)
IZFor example, (a) below lacks such a reading
(a) Several men danced with few women
5 A C C G I m p l e m e n t a t i o n
This section describes a CCG approach to deriving scoped logical forms so that they range over only grammatical readings
We will not discuss details of how CCG charac- terizes natural language syntactically, and refer the interested reader to Steedman (1993) CCGs make use of a limited set of combinators, type raising (T), function composition (B), and function substitution (S), with directionality of combination for syntac- tic grammaticality For the examples in this pa- per, we only need type raising and function composi- tion, along with function application The following shows rules of derivation that we use Each rule is associated with a label, such as > or <B etc, shown
at the end
(15) (a) x / v ~ => x (>) (b) Y x\~ => x (<)
(c) x / v Y/Z => x / z (>a) (d) Y\z x\Y ffi> x \ z (<e) (e) np => T/(T\np) (>T) (f) np => T\(T/np) (<T)
The mapping from syntax to semantics is usually defined in two different ways One is to use ele- mentary categories, such as np or s, in encoding both syntactic types and logical forms (Jowsey, 1990; Steedman, 1990; Park, 1992) The other is to asso- ciate the entire lexical category with a higher-order expression (Kulick, 1995) In this paper, we take the former alternative to describe a first-order rendering
of CCG
Some lexical entries for every are shown below (16) ( s : q - e v e r y (X, N, S ) / ( s : S \ n p : I ) ) / n : X ' N
(17) (s : S/(a : Sknp: s-every(1) ) )/n:W The information ( s / ( s \ n p ) ) / n encodes the syntac- tic fact that every is a constituent which, when
a constituent of category n is provided on its right, returns a constituent of category s / ( s \ n p )
q - e v e r y ( X , l i , S ) is a term for scoped logical forms
We are using different lexical items, for instance
q - e v e r y and e - e v e r y for every, in order to signify their semantic differences 14 These lexical entries are just two instances of a general schema for type- raised categories of quantifiers shown below, where
T is an arbitrary category
(18) (T/(T\np))/na~d (T\(T/np))/n And the semantic part of (16) and (17) is first-order encoding of (19) (a) and (b), respectively 15
14q-every represents every as a quantifier, and
s - e v e r y , as a set denoting property We will
use s-every(l^man(X)) and its ~-reduced equivalent s-every(man) interchangeably
1as-quantifier(noun) denotes an arbitrary set N of individuals d such that d has the property noun and that the cardinality of N is determined by q u a n t i f i e r (and
2 0 8
Trang 5(19) (a) ~n.AP.Vz E s-every(n).P(=)
(b)
(a) encodes wide scope type raising and (b), narrow
With standard entries for verbs as in (20), logical
f o r m s such as (21) and (22) are po ible
(20) saw :- (s:sav(I,Y)\np:X)/np:¥
(21) q-two (X, rep (X), aaw(X, s - f ottr (samp)) )
(22) q-two(X,rep(X) ,q-four(Y,samp(Y),aaw(][,¥)))
Figure 1 shows different ways of deriving
scoped logical forms In (a), n : I ' ! unifies with
n : X ' g i r l ( X ) , so that Ii gets the value g i r l ( X )
This value of !1 is transferred to the expression
s : e v o r y ( X , l i , S ) by partial execution (Pereira
Shieber, 1987; Steedman, 1990; Park, 1992) (a)
shows a derivation for a reading in which object NP
takes wide scope and (b) shows a derivation for a rea-
ding in which subject NP takes wide scope There
are also other derivations
Figure 2 shows logical forms that can be derived in
the present framework from Geach's sentence No-
tice that the conjunction forces subject NP to be first
composed with the verb, so that subject NP must be
type-raised and be combined with the semantics of
the transitive verb As noted earlier, the two catego-
ries for the object still make both scope possibilities
available, as desired The following category is used
for but
(23) ((s : and(P ,1~)/np:][)\ (s:P/np:][))/(s :Q/np :][)
Readings that involve intercalating quantifiers, such
as the one where every girl outscopes one sazopho-
nist, which in turn outscopes most bogs, are correctly
excluded
Figure 3 shows two different derivations of logi-
cal forms for the complex NP two representatives of
three companies (a) shows a derivation for a rea-
ding in which the modifying NP takes wide scope
and (b) shows the other case In combination with
derivations involving transitive verbs with subject
and object NPs, such as ones in Figure 1, this cor-
rectly accounts for four grammatical readings for (5)
(a) 16
Figure 4 shows a derivation for a reading, among
six, in which most customers outscopes every dealer
which in turn outscopes three cars Some of these
readings become unavailable when the sentence con-
tains coordinate structure, such as one below
(24) Every dealer shows most customers (at most)
three cars but most mechanics every car
noun) We conjecture that this can also be made to cap-
ture several related NP-semantics, such as collective NP-
semantics and/or referential NP-semantics, though we
can not discuss further details here
lSAs we can see in Figure 3 (a) (b), there m no
way quantifiers inside $ can be placed between the two
quantifiers two & three, correctly excluding the other
two readings
In particular, (24) does not have those two readings
in which every dealer intercalates most customers and three cars This is exactly predicted by the pre-
sent CCG framework, extending Geach's observa- tion regarding (6) (a), since the coordination forces
the two NPs, most customers and three cars, to be
composed first (Dowty, 1988; Steedman 1990; Park 1992) (25) through (27) show one such derivation,
which results in readings where three cars outscopes most customers but every dealer must take either wide or narrow scope with respect to both most cu- stomers and three cars
(25) -oat cuato.ers
(26)
(2T)
((s:q-most(Z,catm'(g),S)~p:g)/np:Y)
\(((s:S\np:X)/np:T)/np:Z)
three cars ( e : q - t h r e e ( Y , c a r ( Y ) , S ) \ n p : l )
\((s:$\np:X)/n]p:f)
a o | t custoaera three cars
<B ( s : q - t h r e e ( ¥ , c a r ( Y ) , q - t t o s t ( Z , c a t m r ( Z ) , S ) )
\np:X)\(((e:S\np:X)/np:T)/np:g) Figure 5 shows the relevant derivation for the frag-
ment investigate two dialects of discussed at end of
previous section It is a conjoinable constituent, but since there is no way of using type-raised category
for two for a successful derivation, two dialects can
not outscope any other NPs, such as subject NP or the modifying NP (Steedman, 1992) This correctly accounts for our intuition that (14) (a) has an ap- parently intercalating reading and that (14) (b) has only two readings However, there is no similar deri-
vation for the fragment of three companies touched,
as shown below
<
n\n (with T =' n\n)
6 C o n c l u d i n g R e m a r k s
We have shown that the range of grammatical rea- dings allowed by sentences with multiple quantified NPs can be characterized by abstraction at function- argument structure constrained by syntactic adja- cency This result is in principle available to other paradigms that invoke operations like QR at LF or type-lifting, which are essentially equivalent to ab- straction The advantage of CCG's very free notion
Trang 6(a) every girl admired one saxophonist
s : q - e v e r y ( X , l S ) n:X'girl(X) (s:adaired(X.Y)~np:X) s:q-one(Y,sax(Y),S)\(s:S/np:Y) / ( s : S \ n p : X ) / n : X ' i /np:¥
s : q - e v e r y ( X , g i r l ( X ) , S ) / ( s : S \ n p : X )
>B
=:q-every(X.girl(X).adaired(X,Y))/np:Y
(b)
s:q-one(Y,sax(Y).q-every(X,girl(X,adaired(X.Y))))
s : q - e v e r y ( X g i r l ( X ) S ) / ( s : S \ n p : X ) (s:adaired(X.Y)~np:l)
/np:Y s:q-every(X,girl(X).adaired(X,Y))/np:Y
one saxophonist
s : S \ ( s : S / n p : s - o n e ( s a x ) )
s : q - e v e r y ( X g i r l ( X ) a d a i r e d ( X s - o n e ( s a x ) ) )
Figure 1: Every girl admired one sazophonist: Two sample derivations
s : q - e v e r y ( X , g i r l ( l ) a d a i r e d ( l Y ) ) / n p : Y > s : S \ ( s : S / n p : s - o n e ( s a x ) )
<
s : a n d ( q - e v e r y ( X , g i r l ( 1 ) , ~ l ~ - ~ l ( l , Y ) ) , q - m o s t ( l , b o y ( 1 ) , d e t e s t e d ( X , Y ) ) ) / n p : Y
(b)
•:and(q-every(x••irl(•)•ad•ired(••s-•ne(•ax)))•q-•••t(X•b•y(X)•detested(••s-•ne(sax))))
every g i r l admired but most boys d e t e s t e d one saxophonist
s : a d a i r e d ( s - e v e r y ( g i r l ) , Y ) / n p : Y ~ s:q-one(Y,sax(Y),S)\(s:S/np:¥) s:and(admired(s-every(girl),Y),detested(s-most(boy),W))/np:Y
s:q-one(Y,sax(Y),and(adaired(s-every(girl),Y),detested(s-most(boy),Y)))
Figure 2: Every girl admire~ but most boys detested, one sazophonist: Two sample derivations
( s : q - t e o ( X | S )
/ ( s : S ~ n p : l ) ) / n : l ' l
n:X'and(rep(X),of(X.Y))/np:Y
>B ( s : q - t v o ( l , a n d ( r e p ( l ) , o f ( X , Y ) ) , S ) / ( s : S \ n p : X ) ) / n p : ¥
( s : q - t h r e e ( C c o m p ( C ) , S 2 ) / ( s : S t \ n p : l ) )
\ ( ( s : S 2 / ( s : S l ~ n p : l ) ) / n p : C )
(b)
a:q-three(C,comp(C).q-two(X.and(rep(X),of(X.C)),S))/(s:S\np:X) two r e p r e s e n t a t i v e s of t h r e e companies
(s:q-twoCX,l,s) n:X'and(rep(i).of(X,Y))/np:Y ( s : S 2 / ( s : S t \ n p : X ) )
/ ( s : S \ n p : i ) ) / n : g ' N \ ( ( s : S 2 / ( s : S t \ n p : X ) ) / n p : s - t h r e e ( c o a p ) )
>B (s:q-two(X.and(rep(X),of(X,Y)),S)/(s:S\np:X))/np:Y
s :q-tgo (X, and(rep(l) ,of (X,s-three (¢oap))) ,S)/(s:S\np:I)
Figure 3: two representatives o/three companies: Two sample derivations
210
Trang 7e v e r y d e a l e r shows h o s t c u s t o n e r s
s:q-every(X,dlr(X),S) (s:ehow(X,Y,g)\np:I) (s:q-nost(Y,cstnr(Y),S)
>B
s:q-every(X,dlr(X),shog(X,Y,g)/np:Z/np:Y
s:q-nost(Y,cstaw(Y),q-every(X,dlr(X),show(X,Y,Z)))/np:g
three cars
s : S \ ( s : S
/ n p : s - t h r e e ( c a r ) )
s:q-nost(Y,cstnr(Y),q-every(X,dlr(X),show(X,Y,s-three(car))))
Figure 4: Every dealer shows most customers three cars: One sample derivation
(s:investigate(X,g)~ap:X)
/np:Y
np:s-two(l) n : l t / ( n : i l ( n : Y ' t n d ( l , o f ( l , Z ) ) ~ n : I 1 )
/ n : i \ n : Y ' d i a l e c t ( Y ) ) /np:g
~ B n: Y'and(dialect (g) ,of (g,z))/np:Z
>B
rip: s - t w o ( Y ' a n d ( d i a l e c t ( ¥ ) , o f ( Y , Z ) ) ) / r i p : Z
~ B (s:investigate(g,s-tuo(Y'and(dialect(Y),of(Y,Z)))\np:X)/np:Z
Figure 5: investigate two dialects of One derivation
of surface structure is that it ties abstraction or the
equivalent as closely as possible to derivation Ap-
parent counterexamples to the generalization can be
explained by the well-known distinction between re-
ferential and quantificational NP-semantics An im-
plementation of the theory for an English fragment
has been written in Prolog, simulating the 2nd order
properties
There is a question of how the non-standard sur-
face structures of CCG are compatible with well-
known conditions on binding and control (including
crossover) These conditions are typically stated on
standard syntactic dominance relations, but these
relations are no longer uniquely derivable once CCG
allows non-standard surface structures We can
show, however, that by making use of the obliquen-
ess hierarchy (of Jackendoff (1972) and much sub-
sequent work) at the level of LF, rather than sur-
face structure, it is possible to state such conditions
(Steedman, 1993)
A c k n o w l e d g e m e n t s
Special thanks to Mark Steedman Thanks also to
Janet Fodor, Beryl Hoffman, Aravind Joshi, Nobo
Komagata, Anthony Kroch, Michael Niv, Charles L
Ortiz, Jinah Park, Scott Prevost, Matthew Stone,
Bonnie Webber, and Michael White for their help
and criticism at various stages of the presented
idea Thanks are also due to the anonymous referees
who made valuable suggestions to clarify the paper
Standard disclaimers apply The work is supported
in part by NSF grant nos IRI91-17110, and CISE
IIP, CDA 88-22719, DARPA grant no N660001-94- C-6043, and ARO grant no DAAH04-94-G0426
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